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3 years ago

Which of the following exponential regression equations best fits the data shown below

Mathematics

2 answers:

Illusion [34]3 years ago

8 0

Answer:

$\text{D. }y = 8.46(3.51)^{x}$

Step-by-step explanation:

The quickest way is probably to do some direct substitution.

First, let's try f(0).

The values of y predicted by the four equations are, respectively, 3.14, 5.32. 10.84, and 8.46.

It looks like C and D are the closest to the observed data.

Now, let's try f(4) on C and D.

C: 10.84(1.77)⁴ = 10.84 × 9.815 = 106.4

D: 8.46(3.51)⁴ = 8.46 × 151.4 = 1284

The best curve is $y = 8.46(3.51)^{x}.$

Art [367]3 years ago

3 0

Answer:

(D) $8.46\cdot 3.51^x$

Step-by-step explanation:

One could run this on a computer and verify the best fit through brute force. The more elegant way is, as usual, to think: What are special values of x for an exponential function? Zero, for starters - anything to the power of zero is 1. The function value for x=0 in the table is 10. Which choices A through D are close to 10 for x=0? Well, (C) and (D), the rest is too far. Next, what is the function value for the next easy one, x=1? The table says 30. Which of (C) and (D) is close to 30 for x = 1. It turns out we can safely exclude (C) because 10.84*1.77 is about 19 and that's way too far from 30. Let's check (D): 8.46*3.51=29.7 - that's quite close. Since there is no other candidate left, I bet my money on (D). Feel free to verify closeness for the other values of x if you are unconvinced yet.

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Answer:

$\frac{3}{2}$ if you're asking for the reciprocal.

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Use the fact that the mean of a geometric distribution is μ= 1 p and the variance is σ2= q p2. A daily number lottery chooses th

butalik [34]

Answer:

a). The mean = 1000

The variance = 999,000

The standard deviation = 999.4999

b). 1000 times , loss

Step-by-step explanation:

The mean of geometric distribution is given as , $\mu = \frac{1}{p}$

And the variance is given by, $\sigma ^2=\frac{q}{p^2}$

Given : $p=\frac{1}{1000}$

= 0.001

The formulae of mean and variance are :

$\mu = \frac{1}{p}$

$\sigma ^2=\frac{q}{p^2}$

$\sigma ^2=\frac{1-p}{p^2}$

a). Mean = $\mu = \frac{1}{p}$

= $\mu = \frac{1}{0.001}$

= 1000

Variance = $\sigma ^2=\frac{1-p}{p^2}$

= $\sigma ^2=\frac{1-0.001}{0.001^2}$

= 999,000

The standard deviation is determined by the root of the variance.

$\sigma = \sqrt{\sigma^2}$

= $\sqrt{999,000}$ = 999.4999

b). We expect to have play lottery 1000 times to win, because the mean in part (a) is 1000.

When we win the profit is 500 - 1 = 499

When we lose, the profit is -1

Expected value of the mean μ is the summation of a product of each of the possibility x with the probability P(x).

$\mu=\Sigma\ x\ P(x)= 499 \times 0.001+(-1) \times (1-0.001)$

= $ 0.50

Since the answer is negative, we are expected to make a loss.

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A dolphin is 42 feet underwater and ascends at a constant rate for 14 seconds until it reaches the surface. Identify and interpr

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